I'm not the type of composer to dutifully write in the style of my teachers. When I came to Ben Johnston in 1984, however, I found that his harmonic concept of tuning (that is, tuning according to what chords he wants, not according to a predetermined scale, or to a single overtone series) offered the perfect solution to the kind of extremely chromatic voice leading I had already been using since I wrote Baptism in 1982. For my first attempt at composing in just intonation, then, I used a rather Johnstonian harmonic conception, but a simple one.

I often begin a work by writing a melody of superparticular ratios: 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, and 5/4, seven pitches which lie within only 221 cents (a slightly large whole-step). A superparticular ratio is a ratio in the form (x+1)/x; that's the joke of the title. I looked for how many harmonic series' were needed to justify each of these superparticular ratios along with the pitch G as 1/1, and found that I needed only five different ones. (I have often ended up basing my just-intonation music on G because I start out thinking in Harry Partch's 43-tone scale, which was centered on G at 392 cps.) Five was sufficient because the series that contained G as fundamental was the same as the ones that contained it as 2nd harmonic, 4th harmonic, and so on.

Every harmony in Superparticular Woman, then, is chosen from a harmonic series, and every harmonic series contains the pitch G, the pivot point of the work. In the chart below, the fundamental of each series lies at the bottom of each column. Going upward, the 3rd harmonic is next, then the 5th, the 7th, the 9th, and in two cases the 11th as well (even-numbered harmonics are omitted because they duplicate harmonics lower in the series):